Asymptotics of linear initial boundary value problems with periodic boundary data on the half-line and finite intervals
dc.contributor.author | Dujardin, G. M. | |
dc.date.accessioned | 2016-02-25T12:43:18Z | |
dc.date.available | 2016-02-25T12:43:18Z | |
dc.date.issued | 2009-08-12 | |
dc.identifier.citation | Dujardin GM (2009) Asymptotics of linear initial boundary value problems with periodic boundary data on the half-line and finite intervals. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465: 3341–3360. Available: http://dx.doi.org/10.1098/rspa.2009.0194. | |
dc.identifier.issn | 1364-5021 | |
dc.identifier.issn | 1471-2946 | |
dc.identifier.doi | 10.1098/rspa.2009.0194 | |
dc.identifier.uri | http://hdl.handle.net/10754/597627 | |
dc.description.abstract | This paper deals with the asymptotic behaviour of the solutions of linear initial boundary value problems with constant coefficients on the half-line and on finite intervals. We assume that the boundary data are periodic in time and we investigate whether the solution becomes time-periodic after sufficiently long time. Using Fokas' transformation method, we show that, for the linear Schrödinger equation, the linear heat equation and the linearized KdV equation on the half-line, the solutions indeed become periodic for large time. However, for the same linear Schrödinger equation on a finite interval, we show that the solution, in general, is not asymptotically periodic; actually, the asymptotic behaviour of the solution depends on the commensurability of the time period T of the boundary data with the square of the length of the interval over. © 2009 The Royal Society. | |
dc.description.sponsorship | The author thanks A.S. Fokas and P.A. Markowich for their ideas and comments on this work. This publication is based on work supported by Award No. KUK-I1-007-43, made by the King Abdullah University of Science and Technology. | |
dc.publisher | The Royal Society | |
dc.subject | Applied mathematics | |
dc.subject | Differential equations | |
dc.subject | Initial boundary value problems | |
dc.subject | Long-time behaviour | |
dc.subject | Periodic data | |
dc.title | Asymptotics of linear initial boundary value problems with periodic boundary data on the half-line and finite intervals | |
dc.type | Article | |
dc.identifier.journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences | |
kaust.grant.number | KUK-I1-007-43 | |
dc.date.published-online | 2009-08-12 | |
dc.date.published-print | 2009-11-08 |